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I saw this paper that talks about phonon sidebands, multiphonon relaxation, and phonon-assisted energy transfer.
I was skimming through each of the equations, but I have problem understanding the formulation of some of them, for example Equation (3.17):
[tex]g_{\pm }(t) = \int d\omega \begin{Bmatrix} n_{\omega }\\ n_{\omega } +1 \end{Bmatrix}exp\left ( \pm i\omega t \right )[/tex]
If I understand correctly, the part in the braces is the Stirling numbers of the second kind. However, it doesn't make sense to me that the bottom number is larger than the top number, because that should only give zero. So is this something else?
EDIT: dear the moderators. I wasn't really sure where this thread belongs. Purely from mathematics, this thread could belong in the math section, but considering that the discussion centers around the physical aspect of a quantum mechanical phenomena, I decided to put this in this section.
I was skimming through each of the equations, but I have problem understanding the formulation of some of them, for example Equation (3.17):
[tex]g_{\pm }(t) = \int d\omega \begin{Bmatrix} n_{\omega }\\ n_{\omega } +1 \end{Bmatrix}exp\left ( \pm i\omega t \right )[/tex]
If I understand correctly, the part in the braces is the Stirling numbers of the second kind. However, it doesn't make sense to me that the bottom number is larger than the top number, because that should only give zero. So is this something else?
EDIT: dear the moderators. I wasn't really sure where this thread belongs. Purely from mathematics, this thread could belong in the math section, but considering that the discussion centers around the physical aspect of a quantum mechanical phenomena, I decided to put this in this section.